Abstract
The Bethe-Salpeter (bs) dynamics of harmonic confinement developed byanm and collaborators over the last three years and already applied with considerable experimental success to various hadron spectra and coupling structures has been significantly improved through (i) a more exact treatment of a certain momentum-dependent operator\(\hat Q_q \) appearing in thebs equation, using the techniques of SO (2, 1) Lie algebra, and (ii) a sharpened definition of theqcd Coulomb term, so as to yield unambiguous values for different flavour sectors. The resulting mass spectra of light\((q\bar q)\) meson towers and semi-heavy\((Q\bar q)\) quarkonia which are most sensitive to the improved treatment of\(\hat Q_q \), reveal excellent agreement with experiment, one in which only slight changes in the reduced spring constant\((\tilde \omega )\) and quark masses (m q ) over the earlier parametrizations are involved. These changes are however found to have a negligible effect on the (already good) numerical values of the other predictions (electroweak and pionic couplings) depending on the\(q\bar q\) andqqq wave functions. A critical assessment of the strong and weak points of this method is madevis-a-vis other related approaches.
Similar content being viewed by others
References
Adylov G Jet al 1977Nucl. Phys. B128 461
Alper Bet al 1980 CERN-EP/80-64
Aukenbrandt Cet al 1983Phys. Rev. Lett. 51 863
Behrends Set al 1983Phys. Rev. Lett. 50 881
Bethe H A and Salpeter E E 1957Handbuch der Physik (Berlin: Springer Verlag)35 88
Bertlman R A and Ono S 1981Z. Phys. C8 271
Bernard Cet al 1983Phys. Rev. D27 227
Binon Fet al 1983 Serpukov Preprint, IHEP 83-106, SERP-E-140
Blumenfeld Aet al 1982Phys. Rev. D26 648
Brodsky S Jet al 1983Phys. Rev. Lett. 51 83
Brown G E and Rho M 1979Phys. Lett. B82 177
Bohm Met al 1982Phys. Rev. D25 223
Carlson C Eet al 1983Phys. Rev. D27 1556
Chodos A 1974Phys. Rev. D10 2594
Chodos A and Thorn C B 1975Phys. Rev. D12 2733
Cox P Tet al 1981Phys. Rev. Lett. 46 871
Critchfield C L 1975Phys. Rev. D12 923
Critchfield C L 1976J. Math. Phys. 17 261
Dally E Bet al 1982Phys. Rev. Lett. 48 375
Feynman R Pet al 1971Phys. Rev. D3 2706 (referred to in the text asFKR)
Fishbane P and Namyslowski J 1980Phys. Rev. D21 2406
Gardero P and Girardi G C 1972Fort. Der. Phys. 20 105
Girardi G C 1972Nuovo Cimento A10 97
Gunion F F and Li L F 1975Phys. Rev. D12 3583
Hamber C J 1982Nucl. Phys. B195 503
Hamber H and Parisi G 1983Phys. Rev. D27 208
Jena S N 1983Pramana 21 247
Kulshreshtha D Set al 1982Phys. Rev. D26 3131
Kulshreshtha D S and Mitra A N 1983Phys. Rev. D28 588
Levy M 1952Phys. Rev. 88 72
Lipps H 1983Phys. Lett. B126 250
Luscher M 1983Nucl. Phys. B219 233
Miller W 1968Lie theory and special functions (New York: Academic Press)
Mitra A N 1981Z. Phys. C8 25
Mitra A N and Santhanam I 1981aZ. Phys. C8 33
Mitra A N and Santhanam I 1981bPhys. Lett. 62
Mitra A N 1982Ann. Phys. 143 365
Mitra A N and Kulshreshtha D S 1982Phys. Rev. D26 3123, 3133
Mitra A N and Ramanathan 1983Phys. Lett. B128 318
Mitra A N and RamanathanR 1984Z. Phys. C (in press)
Mitra A N and Ono S 1983 Th. 3707-CERN (to be published)
Mitra A N and Mittal A 1984Phys. Rev. D29 (in press)
Mittal A and Mitra A N 1984Phys. Rev. D29 (in press)
Ono S and Schoberl F 1982Phys. Lett. B118 419
Particle Data Group 1982Phys. Lett. B111 1
Pennington M R 1983Rep. Progr. Phys. 46 393
Rein D W 1977Nuovo Cimento A38 19
Rosenzweig C 1982Z. Phys. C14 179
Smith G B and Tassie L F 1975Ann. Phys. 65 352
Thomas A Wet al 1981Phys. Rev. D24 216
Zhu Wei 1982Commun. Theor. Phys. 1 597
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mitra, A.N., Mittal, A. Complete mass spectra of\(q\bar q\) and\(Q\bar q\) mesons with improved Bethe-Salpeter dynamics of confinementmesons with improved Bethe-Salpeter dynamics of confinement. Pramana - J Phys 22, 221–235 (1984). https://doi.org/10.1007/BF02846375
Issue Date:
DOI: https://doi.org/10.1007/BF02846375